Resolution measurement in structures derived from single particles

Analytical expressions are derived and computer simulations are presented to assess the accuracy of procedures commonly used to estimate the resolution of three-dimensional (3D) structures derived from images of single protein molecules or complexes. It is shown that in the case of a low signal-to-noise ratio in the images, the Fourier ring correlation between two structures, each calculated using one half of the data, significantly overestimates the resolution when the two half data sets were aligned against the same reference structure. The overestimate arises because of a correlation between the noise components present in the images. The correlation is introduced by the alignment and becomes more serious as the signal-to-noise ratio is reduced. A reliable resolution measure is only obtained when the two half data sets are aligned against two independent reference structures. It is further shown that the noise correlation also significantly affects the spectral signal-to-noise ratio and the Q factor, making them unreliable measures of signal present in a 3D structure and in the original images, respectively. It is concluded that the alignment of images is always accompanied by a correlation of the noise and that this correlation is indistinguishable from a correlation arising from a signal.